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Linear-quadratic control for stochastic equations in a Hilbert space with a fractional Brownian motion
Duncan, Tyrone E. ; Maslowski, Bozenna J. ; Pasik-Duncan, Bozenna
Duncan, Tyrone E.
Maslowski, Bozenna J.
Pasik-Duncan, Bozenna
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Abstract
A linear-quadratic control problem with a finite time horizon for some infinite-dimensional controlled stochastic differential equations driven by a fractional Gaussian noise is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well-known linear feedback control for the associated deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system response to the future noise. The covariance of the noise as well as the control operator in the system equation can in general be unbounded, so the results can also be applied where the noise or the control are on the boundary of the domain or at discrete points in the domain. Some examples of controlled stochastic partial differential equations are given.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/110831416.
Date
2012-01-01
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Society for Industrial and Applied Mathematics
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Keywords
linear-quadratic control, fractional Brownian motion, stochastic partial differential equations
Citation
Duncan, Tyrone E. "Linear-quadratic control for stochastic equations in a Hilbert space with a fractional Brownian motion." SIAM J. Control Optim. (2012) 50 , 1. 507-531. http://www.dx.doi.org/10.1137/110831416.